File size: 20,331 Bytes
93d7919 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 | {
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "14007fc2-be2a-497a-940d-4330bf2b46d3",
"metadata": {},
"outputs": [],
"source": [
"# Imports\n",
"\n",
"from pgmpy.models import DynamicBayesianNetwork as DBN\n",
"from pgmpy.factors.discrete import TabularCPD"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "9d5ea2e4-a280-4622-9045-13bc2b4cce2a",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "06cfdf96f46c42c2a833c5021bd71a43",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
" 0%| | 0/40 [00:00<?, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: 1.1102230246251565e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n",
"WARNING:pgmpy:Probability values don't exactly sum to 1. Differ by: -2.220446049250313e-16. Adjusting values.\n"
]
}
],
"source": [
"# Initialize a simple DBN model modeling the Weather (W), Rain (O), Temperature (T), and Humidity (H).\n",
"\n",
"dbn = DBN()\n",
"\n",
"# pgmpy requires the user to define the structure of the first time slice and the edges connecting the first time slice to the second time slice.\n",
"# pgmpy assumes that this structure remains constant for further time slices, i.e., it is a 2-TBN.\n",
"\n",
"# Add intra-slice edges for both time slices\n",
"dbn.add_edges_from([\n",
" (('W', 0), ('O', 0)), # Weather influences ground observation\n",
" (('T', 0), ('H', 0)), # Temperature influences humidity\n",
" (('W', 0), ('H', 0)) # Weather influences humidity\n",
"])\n",
"\n",
"# Add inter-slice edges\n",
"dbn.add_edges_from([\n",
" (('W', 0), ('W', 1)), # Weather transition\n",
" (('T', 0), ('T', 1)), # Temperature transition\n",
" (('W', 0), ('T', 1)) # Weather influences future temperature\n",
"])\n",
"\n",
"# Define the parameters of the model. Again pgmpy assumes that these CPDs remain the same for future time slices.\n",
"\n",
"# Define CPDs\n",
"# CPD for W (Weather transition)\n",
"cpd_w_0 = TabularCPD(\n",
" variable=('W', 0),\n",
" variable_card=3, # Sunny, Cloudy, Rainy\n",
" values=[[0.6], [0.3], [0.1]], # Initial probabilities\n",
")\n",
"\n",
"cpd_w_1 = TabularCPD(\n",
" variable=('W', 1),\n",
" variable_card=3,\n",
" evidence=[('W', 0)],\n",
" evidence_card=[3],\n",
" values=[\n",
" [0.7, 0.3, 0.2], # P(Sunny | W_0)\n",
" [0.2, 0.4, 0.3], # P(Cloudy | W_0)\n",
" [0.1, 0.3, 0.5] # P(Rainy | W_0)\n",
" ],\n",
")\n",
"\n",
"# CPD for T (Temperature transition)\n",
"cpd_t_0 = TabularCPD(\n",
" variable=('T', 0),\n",
" variable_card=3, # Hot, Mild, Cold\n",
" values=[[0.5], [0.4], [0.1]] # Initial probabilities\n",
")\n",
"\n",
"cpd_t_1 = TabularCPD(\n",
" variable=('T', 1),\n",
" variable_card=3,\n",
" evidence=[('T', 0), ('W', 0)],\n",
" evidence_card=[3, 3],\n",
" values=[\n",
" [0.8, 0.6, 0.1, 0.7, 0.4, 0.2, 0.6, 0.3, 0.1], # P(Hot | T_0, W_0)\n",
" [0.2, 0.3, 0.7, 0.2, 0.5, 0.3, 0.3, 0.4, 0.3], # P(Mild | T_0, W_0)\n",
" [0.0, 0.1, 0.2, 0.1, 0.1, 0.5, 0.1, 0.3, 0.6] # P(Cold | T_0, W_0)\n",
" ]\n",
")\n",
"\n",
"# CPD for O (Ground observation)\n",
"cpd_o = TabularCPD(\n",
" variable=('O', 0),\n",
" variable_card=2, # Dry, Wet\n",
" evidence=[('W', 0)],\n",
" evidence_card=[3],\n",
" values=[\n",
" [0.9, 0.6, 0.2], # P(Dry | Sunny, Cloudy, Rainy)\n",
" [0.1, 0.4, 0.8] # P(Wet | Sunny, Cloudy, Rainy)\n",
" ]\n",
")\n",
"\n",
"# CPD for H (Humidity observation)\n",
"cpd_h = TabularCPD(\n",
" variable=('H', 0),\n",
" variable_card=3, # Low, Medium, High\n",
" evidence=[('T', 0), ('W', 0)],\n",
" evidence_card=[3, 3],\n",
" values=[\n",
" [0.7, 0.4, 0.1, 0.5, 0.3, 0.2, 0.3, 0.2, 0.1], # P(Low | T_0, W_0)\n",
" [0.2, 0.5, 0.3, 0.4, 0.5, 0.3, 0.4, 0.3, 0.2], # P(Medium | T_0, W_0)\n",
" [0.1, 0.1, 0.6, 0.1, 0.2, 0.5, 0.3, 0.5, 0.7] # P(High | T_0, W_0)\n",
" ]\n",
")\n",
"\n",
"# Add CPDs to the DBN\n",
"dbn.add_cpds(cpd_w_0, cpd_w_1, cpd_t_0, cpd_t_1, cpd_o, cpd_h)\n",
"\n",
"# After defining the model, call the initialization method that generates the required data structures for further computation.\n",
"dbn.initialize_initial_state()\n",
"\n",
"# Simulate some data from the defined model.\n",
"samples = dbn.simulate(n_samples=1000, n_time_slices=10)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "7bf63016-f566-49cf-bd43-87c571b5f1c6",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:pgmpy: Datatype (N=numerical, C=Categorical Unordered, O=Categorical Ordered) inferred from data: \n",
" {'T_0': 'C', 'W_0': 'C', 'H_0': 'C', 'O_0': 'C', 'T_1': 'C', 'W_1': 'C', 'H_1': 'C', 'O_1': 'C'}\n",
"INFO:pgmpy: Datatype (N=numerical, C=Categorical Unordered, O=Categorical Ordered) inferred from data: \n",
" {'T_0': 'C', 'W_0': 'C', 'H_0': 'C', 'O_0': 'C', 'T_1': 'C', 'W_1': 'C', 'H_1': 'C', 'O_1': 'C'}\n",
"INFO:pgmpy: Datatype (N=numerical, C=Categorical Unordered, O=Categorical Ordered) inferred from data: \n",
" {'T_0': 'C', 'W_0': 'C', 'H_0': 'C', 'O_0': 'C', 'T_1': 'C', 'W_1': 'C', 'H_1': 'C', 'O_1': 'C'}\n",
"INFO:pgmpy: Datatype (N=numerical, C=Categorical Unordered, O=Categorical Ordered) inferred from data: \n",
" {'T_0': 'C', 'W_0': 'C', 'H_0': 'C', 'O_0': 'C', 'T_1': 'C', 'W_1': 'C', 'H_1': 'C', 'O_1': 'C'}\n",
"INFO:pgmpy: Datatype (N=numerical, C=Categorical Unordered, O=Categorical Ordered) inferred from data: \n",
" {'T_0': 'C', 'W_0': 'C', 'H_0': 'C', 'O_0': 'C', 'T_1': 'C', 'W_1': 'C', 'H_1': 'C', 'O_1': 'C'}\n",
"INFO:pgmpy: Datatype (N=numerical, C=Categorical Unordered, O=Categorical Ordered) inferred from data: \n",
" {'T_0': 'C', 'W_0': 'C', 'H_0': 'C', 'O_0': 'C', 'T_1': 'C', 'W_1': 'C', 'H_1': 'C', 'O_1': 'C'}\n",
"INFO:pgmpy: Datatype (N=numerical, C=Categorical Unordered, O=Categorical Ordered) inferred from data: \n",
" {'T_0': 'C', 'W_0': 'C', 'H_0': 'C', 'O_0': 'C', 'T_1': 'C', 'W_1': 'C', 'H_1': 'C', 'O_1': 'C'}\n",
"INFO:pgmpy: Datatype (N=numerical, C=Categorical Unordered, O=Categorical Ordered) inferred from data: \n",
" {'T_0': 'C', 'W_0': 'C', 'H_0': 'C', 'O_0': 'C', 'T_1': 'C', 'W_1': 'C', 'H_1': 'C', 'O_1': 'C'}\n",
"INFO:pgmpy: Datatype (N=numerical, C=Categorical Unordered, O=Categorical Ordered) inferred from data: \n",
" {'T_0': 'C', 'W_0': 'C', 'H_0': 'C', 'O_0': 'C', 'T_1': 'C', 'W_1': 'C', 'H_1': 'C', 'O_1': 'C'}\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[<TabularCPD representing P((W, 0):3) at 0x747250050110>, <TabularCPD representing P((O, 0):2 | (W, 0):3) at 0x74713dd92570>, <TabularCPD representing P((H, 0):3 | (T, 0):3, (W, 0):3) at 0x74713dd93230>, <TabularCPD representing P((W, 1):3 | (W, 0):3) at 0x74713dd92ea0>, <TabularCPD representing P((T, 1):3 | (T, 0):3, (W, 0):3) at 0x74713dd925a0>, <TabularCPD representing P((O, 1):2 | (W, 1):3) at 0x74713dd93590>, <TabularCPD representing P((H, 1):3 | (T, 1):3, (W, 1):3) at 0x74713dd917c0>, <TabularCPD representing P((T, 0):3) at 0x74713dd927e0>]\n"
]
}
],
"source": [
"# Fitting model parameters to a defined network structure.\n",
"\n",
"# Define the network structure for which to learn the model parameters. Here, we have assumeed the same model\n",
"# structure that we simulated the data from\n",
"dbn = DBN()\n",
"dbn.add_edges_from([\n",
" (('W', 0), ('O', 0)), # Weather influences ground observation\n",
" (('T', 0), ('H', 0)), # Temperature influences humidity\n",
" (('W', 0), ('H', 0)) # Weather influences humidity\n",
"])\n",
"dbn.add_edges_from([\n",
" (('W', 0), ('W', 1)), # Weather transition\n",
" (('T', 0), ('T', 1)), # Temperature transition\n",
" (('W', 0), ('T', 1)) # Weather influences future temperature\n",
"])\n",
"\n",
"# Fit the model using simulated samples\n",
"dbn.fit(samples)\n",
"print(dbn.cpds)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "bfd51960-dda5-40ea-a0e6-499e490c699e",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/tmp/ipykernel_1736345/1916813029.py:18: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
" df_long = pd.concat([df_long, samples_t])\n",
"/tmp/ipykernel_1736345/1916813029.py:18: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
" df_long = pd.concat([df_long, samples_t])\n",
"/tmp/ipykernel_1736345/1916813029.py:18: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
" df_long = pd.concat([df_long, samples_t])\n",
"/tmp/ipykernel_1736345/1916813029.py:18: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
" df_long = pd.concat([df_long, samples_t])\n",
"/tmp/ipykernel_1736345/1916813029.py:18: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
" df_long = pd.concat([df_long, samples_t])\n",
"/tmp/ipykernel_1736345/1916813029.py:18: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
" df_long = pd.concat([df_long, samples_t])\n",
"/tmp/ipykernel_1736345/1916813029.py:18: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
" df_long = pd.concat([df_long, samples_t])\n",
"/tmp/ipykernel_1736345/1916813029.py:18: FutureWarning: The behavior of DataFrame concatenation with empty or all-NA entries is deprecated. In a future version, this will no longer exclude empty or all-NA columns when determining the result dtypes. To retain the old behavior, exclude the relevant entries before the concat operation.\n",
" df_long = pd.concat([df_long, samples_t])\n",
"INFO:pgmpy: Datatype (N=numerical, C=Categorical Unordered, O=Categorical Ordered) inferred from data: \n",
" {'T0': 'C', 'W0': 'C', 'H0': 'C', 'O0': 'C', 'T1': 'C', 'W1': 'C', 'H1': 'C', 'O1': 'C'}\n",
"INFO:pgmpy: Datatype (N=numerical, C=Categorical Unordered, O=Categorical Ordered) inferred from data: \n",
" {'T0': 'C', 'W0': 'C', 'H0': 'C', 'O0': 'C', 'T1': 'C', 'W1': 'C', 'H1': 'C', 'O1': 'C'}\n",
"INFO:pgmpy: Datatype (N=numerical, C=Categorical Unordered, O=Categorical Ordered) inferred from data: \n",
" {'T0': 'C', 'W0': 'C', 'H0': 'C', 'O0': 'C', 'T1': 'C', 'W1': 'C', 'H1': 'C', 'O1': 'C'}\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "5951e44f9bc644fabf1c69e75b069379",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
" 0%| | 0/1000000 [00:00<?, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[('T0', 'T1'), ('W0', 'T1'), ('W0', 'H0'), ('W0', 'W1'), ('W0', 'T0'), ('H0', 'T0'), ('O0', 'W0'), ('T1', 'H1'), ('W1', 'H1'), ('W1', 'O1')]\n"
]
}
],
"source": [
"# Learning the model structure from data.\n",
"\n",
"# pgmpy doesn't implement any specific methods for DBN structure learning. This is a hackish method to utilize the \n",
"# existing BN learning algorithms to estimate the structure of the DBN. Essentially, we remove the time-information from the\n",
"# given data and try to learn the 2-DBN network that remains constant across time-slices.\n",
"\n",
"# First convert the given dataset into long form removing the time information such that it is suitable to learn the 2-DBN network.\n",
"\n",
"import pandas as pd\n",
"\n",
"colnames = [(node + '0') for node in dbn._nodes()] + [(node + '1') for node in dbn._nodes()]\n",
"df_long = pd.DataFrame(columns=colnames)\n",
"\n",
"for t in range(9):\n",
" cols = [(node, t) for node in dbn._nodes()] + [(node, t+1) for node in dbn._nodes()]\n",
" samples_t = samples.loc[:, cols]\n",
" samples_t.columns = colnames\n",
" df_long = pd.concat([df_long, samples_t])\n",
"\n",
"df_long = df_long.reset_index(drop=True)\n",
"\n",
"\n",
"# Use this long data frame to learn the first two time frames of the DBN. Because we are using structure learning algorithms we\n",
"# need to add constraints such that the algorithm doesn't learn edges from time slice 1 to 0.\n",
"from pgmpy.estimators import HillClimbSearch\n",
"est = HillClimbSearch(df_long)\n",
"dag = est.estimate(black_list=[('W1', 'W0'), ('W1', 'O0'), ('W1', 'T0'), ('W1', 'H0'),\n",
" ('O1', 'W0'), ('O1', 'O0'), ('O1', 'T0'), ('O1', 'H0'), \n",
" ('T1', 'W0'), ('T1', 'O0'), ('T1', 'T0'), ('T1', 'H0'), \n",
" ('H1', 'W0'), ('H1', 'O0'), ('H1', 'T0'), ('H1', 'H0'),]) # Constraints to learn edges in only time forward direction.\n",
"\n",
"print(dag.edges()) # Use this learned DAG to define a DBN."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.4"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
|